Another problematic feature of inflation is that one often ignores the pre-inflationary dynamics and
sets the Bunch-Davies (BD) vacuum,
and it is not clear how such a vacuum state can be realized dynamically in the framework of quantum cosmology [1]}, considering the fact that a pre-inflationary phase always exists between the Plank
and inflation scales, which are about \(10^3 \sim 10^{12}\)  orders of magnitude difference [2]}, [1]}.
While these problems of inflationary paradigm demand a completion from quantum theory of spacetimes, they also open an avenue to overcome one of the main obstacles in the development of quantum gravity,
which concerns with the lack of experimental evidences. Thus, understanding inflation in the framework of quantum gravity could offer valuable guidances to the construction of the underlying theory [4]}, [5]}, [6]}.
